Peter Stines, When a Confederate cavalry trooper`s horse came up lame, for what ever reason (sore back, cracked hooves, bad leg, illness, disease), or was shot from under him in battle or skirmish, he was required to get another horse at his own cost. Until he did he was no longer qualified for cavalry service and was often given odd jobs around camp that he could do, often times regarded as detached, special or extra duty. Some times a trooper under these circumstances was sent to the supply train`s or even placed on detached service at other post`s or camp`s until a horse could be obtained and be able to qualify for cavalry service again. Some times the trooper`s service record will reflect that he was without a horse for a specific amount of time and other times not. Or due to advanced age and physical disability and found not able to perform cavalry service a trooper may be assigned to a duty that he can do, such as a Teamster, or released on a surgeons certificate and sent home for the remainder of the war.
Since your ancestor`s service records reflect that he was specifically told to apply for a discharge in 1862, and had appeared before a judge to testify to his age and ability to perform his duty (fitness evaluation), in addition to his "rheumatism" condition, I would say that his superior officers questioned his ability to continue his cavalry service and he was given the option of being sent home for the remainder of the war, due to his limitations, or find a job that he could perform so that he could remain and continue to serve the southern cause... He chose to remain.
I have found several such cases in my research regarding the 2nd Regiment Alabama Cavalry, where officers, non-commissioned officers and privates were approaching 50 or older and could no longer perform their duty and were either sent home on surgeon certificates or reassigned to other duties and positions, such as administrative, with the same regiment or sent up to headquarters on the brigade or division level.